Beam clean-up and combining via stimulated scattering in liquid crystals

B.Ya. Zeldovich, I.V. Ciapurin L.B. Glebov, C. Tsai, M.C. Stickley,

School of Optics / CREOL, University of Central Florida, 4000 Central Florida Blvd., Orlando FL 32816-2700 Phone (407) 823-6831, FAX (407) 823-6880, boris@creol.ucf.edu

Abstract: Orientational stimulated scattering from o-wave into e-wave in liquid crystal may combine coherent beams or modes of amplifier(s) into diffraction-limited output. In experiment a 1000 micron liquid crystal layer transmitted undistorted o-wave with low attenuation. 2000 Optical Society of America OCIS codes: (140.3300) Laser beam shaping, (160.3710) Liquid crystals, (190.5890) Scattering, stimulated

1. Introduction

Modern diode-pumped fiber lasers and solid-state lasers can work in the regime of Power Amplifiers (PA) and thus provide output power in the scale of Kilowatt and more. Crucial problem exists of making a beam of diffraction quality out of resultant radiation. Combining the outputs of several fiber lasers, when each of them is fed by the same signal from Master Oscillator (MO), and each works on a single transverse mode, may be done by multibeam analogs of Mach-Zender interferometer. The phase of each of the beams there is to be controlled electro-optically. However, clean-up of a beam with distorted (albeit coherent) transverse structure, as well as combining several such beams can not be done directly by the interferometric schemes.

We suggest here the device to clean-up and combine transversely and mutually coherent beams of possibly distorted transverse structure into one diffraction-quality beam. The process in question is Stimulated Orientational Scattering from e-wave into o-wave in a cell with Nematic Liquid Crystal (NLC).

Fig. 1. Interference of distorted pump wave (Ee in our case) with the diffraction-quality signal beam (Eo in our case) results in the change of orientation of NLC’s director. Scattering of pump into signal by this grating yields energy transfer with the preservation of beam quality.

2. Theoretical estimations Energy exchange via Stimulated Scattering of light is characterized by gain coefficient

g[1/m, intensity] =G⋅Se,o , (1)

where S is Poynting vector of the wave. Stimulated Scattering by orientation gratings in NLC has this value of gain constant G, see [1, 2]:

( )cnnK

nnncnqK

nnGeo22

2oevac

oe2

22

22o

2e

vac

12

1

+≡−=

πλ

λπ (2)

z

Eo

Ee

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Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

Here Se,o = 0.5cne,oε0|Ee,0s|2 are the values of the Poynting vector of the corresponding waves (Watt/m2), and the coefficient G (m/Watt) gives the intensity gain g of the signal at the optimal frequency shift Γ = +Ω, so that So(z)= S0(0)exp(gz) in the approximation of the undepleted pump, which is e-wave in our case. . The value of G is

( )cnnK

nnncnqK

nnGeo22

2oevac

oe2

22

22o

2e

vac

12

1

+≡−=

πλ

λπ . (2)

This kind of steady state stimulated scattering in a planar NLC cell has been observed in [3, 4] in complete agreement with theory. Taking λvac = 1 µm, elastic constant of NLC K22 = 4⋅10−12 Joule/m, refractive index n≈1.5, one gets G = 6⋅10−4 m/Watt ≡ 0.06 cm/Watt. It means that the undepleted amplification factor for the intensity of the signal at the thickness of the cell L = 500 µm and for the pump Poynting vector Sp = 3⋅103 Watt/cm2 is exp(GSpL) = e9 = 0.8⋅104. We have all the reasons to assume that such an amplification factor will be quite sufficient for almost complete energy transfer from the multi-transverse-mode pump into the clean signal beam. The relaxation time τ = 1/Γ depends on the value of the optical anisotropy and on the orientational viscosity of the NLC that is chosen. Taking, for example, ne – no = 0.2 and η = 0.1 Pa⋅sec, one gets Γ = K22(ne – no)2 (2π/λvac)2/η = 63 rad/s, Ωopt/2π =Γ/2π = 10 Hz, τ = 1/Γ = 16 millisecond. That requires that the phase shift between various pump beams or modes should not drift more than 1 radian during 20 millisecond or so. Determining whether this is possible requires physical experiments with the particular laser set-up.

3. Preliminary experimental set-up We have prepared a cell with Nematic Liquid Crystal of planar orientation. Special configuration of the cell: the

thickness changed from 100 micron to 1000 micron at the distance about 48 mm, resulting in a birefringent wedge (mini-prism), which allows to study energy transfer and propagation properties at different values of interaction thickness L. Fig. 2 shows propagation of o-wave (left picture) and e-wave (right picture) through 750 microns 0f NLC in the region with rather strong distortions. One sees that o-wave remains practically un-distorted, in agreement with earlier predictions [5] and experiments [6]. Sure, there were regions of the cell with smaller distortions even for e-wave.

Fig. 2. Un-distorted transmission of ordinary wave (left) and rather strong distortions in the transmission of extraordinary wave (right) through “bad spot” with the thickness 750 microns of planar NLC cell.

We made preliminary measurements of extinction coefficient by this NLC at λ = 632 nm. Since we can not

distinguish between actual absorption, extinction due to scattering, and other loss, our estimation is Re ≤ 9 [1/cm and Ro ≤ 8 [1/cm] respectively. Scattering in LNC scales approximately as 1/λ2 , and therefore we can expect about 4 times smaller scattering at λ = 1.06 micron. In the talk we will present the results of the study of beam clean-up.

To conclude, the possibility of beam clean-up via stimulated scattering in Liquid Crystals seems realistic.

References 1. B. Ya. Zeldovich, A. V. Sukhov, N. V. Tabirian, The Orientational Optical Nonlinearity of Liquid Crystals, Special issue of Mol. Cryst. &

Liq. Cryst. 136, #1, 140 pages, 1986. 2. I. C. Khoo, Liquid crystals: physical properties and nonlinear optical phenomena New York, N.Y. : Wiley & Sons, c1995. 3. I. I. Goosev, et al., Sov. Phys. JETP Lett., 55, 178-183 (1992). 4. A. V. Sukhov, N. V. Tabirian, B. Ya. Zeldovich, JOSA B, 18, #8, 1203 (2001) 5. N. B. Baranova, B. Ya. Zeldovich, , Sov. Phys. JETP Lett. 32, 622 (1980). 6. N. B. Baranova et al., Mol. Cryst. & Liq. Cryst. 210, 155 (1992).

1

Beam clean-up and combining via stimulated scattering

in liquid crystalsI. V. Ciapurin, L. B. Glebov, C. Tsai, M. C. Stickley,

B. Ya. Zeldovich

School of Optics / CREOL, University of Central Florida,

Orlando, Florida

CLEO’2003, Baltimore, June 04.

2

Overview of the talk1. High-power CW solid-state and fiber lasers are here ! 2. Combining several beams and beam clean-up are

important problems. 3. Idea: to combine several mutually coherent beams or

angular components via Stimulated Scattering.4. Particular design: Liquid Crystal with o-type signal

wave and e-type pump wave.5. Estimations of the required power and heat transfer.6. Experimental set-up.7. Demonstration of Orientational Stimulated Scattering8. Conclusion.

3

High-power CW solid-state and fiber lasers are here !

They have the power more than 1000 Watt now

and promise much more.

Beam clean-up and combining the energy from

several amplifiers look attractive.

However, Louiville’s (Lagrange-Helmholtz) theorem

does not permit to increase brightness

by linear-optical devices.

4

Stimulated Scattering:coherent amplification of signal beam

via energy transfer from the pump beam

Pump beam

High quality weak

signal beam

5

Suggested in this work: to use orientational Stimulated

Scattering in a Nematic Liquid Crystal

Es

ks

Epkp

BA

z

Signal plane wave Esand inhomogeneous pump wave Ep have slightly different frequencies, ωp−ωs=Ω. They illuminate liquid crystal cell with a planar orientation of the director.

6

BA

θ

x

y

Interference of Es and Ep yields the grating with director orientation δd∝ exp[iΩt−i(kp−ks)⋅r]. Scattering of the pump Ep by this grating of dielectric permittivity results in amplification of the signal Es.

Grating-type Orientational Nonlinearity (GRON) in a Nematic Liquid Crystal

References on stimulated scattering in LC:

N. V. Tabirian, A. V. Sukhov, B. Ya. Zeldovich, M.C.L.C. 136, #1, pp. 1-140, 1986.I. I. Goosev et al., JETP Lett., 55, p. 178, 1992.I. C. Khoo et al., Optics Lett., 20, p. 130, 1995.N. V. Tabirian, A. V. Sukhov, B. Ya. Zeldovich, JOSA B, 18, pp. 1203-06, 2001(well-saturated regime at pump level about 0.5 Watt for λ = 1.06 µm)

7

System of basic equations in steady-state approximation

Here Ep is pump field, Es is signal field,

Sp, Ss are the corresponding values

of Poynting vector, G is the gain constantat the “optimum” frequency shift Ω = Γ.

( )[ ] ( )[ ]s2p

pp2s

s

])/(1[/,

])/(1[/ SiGE

zE

SiGEzE

ΓΩ+−ΓΩ

−=∂∂

ΓΩ+−ΓΩ

=∂∂

( )cnnK

nnncnqK

nnGeo22

2oevac

oe2

22

22o

2e

vac

12

1⎟⎠⎞

⎜⎝⎛ +

≡−=πλ

λπ

8

Estimations

For NLC with ne–no = 0.2, λvac = 1 µm,

K22 = 4⋅10−11 Newton (4⋅10−6 dyne), n≈1.5,

one gets G = 6⋅10−5 m/Watt.

Taking cell thickness L = 0.5 mm,

pump Poynting vector

Sp = 30 KWatt/cm2 ≡ 3⋅108 Watt/m2,

one gets signal amplification

exp(GSpL) = e9 ≈ 104.

9

Estimations of thermal load

If we take an estimation of the true absorption coefficient, α ≈ 0.01 m−1 ≡ 0.0001 cm−1, then the fraction of the light absorbed in the L=500-micron layer is about f=αL≈5⋅10−5. At the value of the incident Poynting vector S of about 30 KWatt/cm2, such an absorption yields a thermal power deposition Sf ≈ 0.15 Watt/cm2 of the beam area.

Taking the order of magnitude of thermal conductivity coefficient for NLC Λ≈1.3⋅10−3 Watt/cm⋅K, and a cell thickness L = 500 micron, we get form the steady-state solution of the thermal conductivity equation: δTcenter =fSL/8Λ ≈ 0.7 K. The flux of thermal power through one of the two sapphire walls, 0.5fS≈0.075 Watt/cm2, can be maintained with a temperature gradient of 0.5fS/Λsapphire = 0.2 K/cm.

10

Experiment

We used LC cell with Nematic Liquid Crystal of planar orientation.

To try various values of thickness of the cell, we used a wedge-type cell, with the thickness

varying from 100 to 1000 micron at 5 cm of length.

Light in

Light out

e-polarization (extra-ordinary type) o-polarization

(ordinary type)

11

Extraordinary wave, λ = 632.8 nm,transmitted trough 800 micron of planar NLC cell.

Distortions are rather strong.

12

Ordinary wave, λ = 632.8 nm,transmitted trough 800 micron of planar NLC cell.

Distortions are practically absent.

13

Reasons for distortion-less transmissionof the ordinary-type wave

1. Polarizations of both ordinary and extra-ordinary waves follow adiabatically the local orientation of director.2. Input and output o- and e-polarizations are prescribed by the boundaries and thus are preserved.3. Phase velocity of the e-wave varies with the variations of the angle αbetween propagation k-vector and director d (ellipsoid ! ).4. Phase velocity of the o-wave is constant at any angle α (sphere ! ).

Therefore o-wave does not acquire ether phase distortions or polarization distortions.

(N. B. Baranova, I. V. Goosev, V. A. Krivoschekov, B. Ya. Zeldovich, Molecular Crystals & Liquid Crystals J., 210, 155, 1992,

Distortionless Propagation of O-wave through Inhomogeneous Nematic (Theory and & Experiment.)

d

kα

14

Observation of Stimulated Grating Orientational Scattering in NLC

λ = 1.08 mkm, Yb-doped IPGfiber laser, output power 100 W, power to the cell 0.8 W.Lens F = 20 cm,beam ∅ = 5 mm (FWe-2M) at the lens.

15

Observation of Stimulated Grating Orientational Scattering in NLC

λ= 1.08 mkm, Yb-doped IPGfiber laser, output power 100 W, power to the cell 3.2 W.Lens F = 20 cm,beam ∅ = 5 mm (FWe-2M) at the lens.Cell was out of focus.

16

Observation of Stimulated Grating Orientational Scattering in NLC

Power to the cell 1.6 W.Lens F = 20 cm,beam ∅ = 5 mm (FWe-2M) at the lens.Cell was in focus.Analyzer transmitted mostly the scattered wave. Almost no o-wave pump is left.

17

Potential problems to be overcome. 1.

Term (–i) means Cross-Phase Modulation (CPM)at the “optimum” frequency shift Ω = Γ.

It may distort the phase of the cleaned signal beam.

( )[ ]p2s

s

])/(1[/ SiGE

zE

ΓΩ+−ΓΩ

=∂∂

Some of the ways to overcome CPM’s influence.Make the profile of pump’s Poynting vector

approximately parabolic.Take “super-optimum” frequency shift, e.g.

Ω = 3Γ. Then gain will be damped by factor 0.6, while CPM will be damped by factor 0.1.

Use double-phase conjugation scheme.

18

Potential problems to be overcome. 2.

Time coherence is required between the signal and the beam(s) to be combined and/or cleaned-up.

Coherence is not an issue, if the spectrum of our MO-PA device is narrow enough.

Equal optical paths for various channels, angular components etc. should be provided within the coherence length.

What to do about it ?

19

1.Stimulated Scattering in Nematic LC is suggested for the beam combining and clean-up.

2. Inhomogeneities of NLC orientation do not distort ordinary wave, even at L = 1 mm.

3. Stimulated scattering at 1.06 µm is demonstrated in the work by Tabirian, Sukhov & Zeldovich,and at 1.08 µm here.

4. NLC cell and LC material within it are shown to tolerate at least 100 KWatt / cm2 of CW light.

5. Perspectives of beam combining and clean-up for high-average power beams look promising.

Conclusions